What is the central idea of "The Taming of the Shrew"(ACT 3)

It is now Saturday, the day before Katherine is scheduled to wed Petruchio. Lucentio and Hortensio, in their respective disguises as Cambio and Litio, are “instructing” Bianca somewhere in Baptista’s house, and the scene begins with the two of them battling for her exclusive attention. Bianca clearly has begun to form a preference, and she ends the dispute by declaring that she will hear her Latin lesson from Lucentio first, while Hortensio tunes his instrument. During the Latin lesson, with Hortensio out of hearing range, Lucentio conveys his true intentions to Bianca through a mock translation of a Latin paragraph. She replies to him, in the same way, that she distrusts him, and yet she does not hide the fact that she is taken with her young suitor. Hortensio tries to break in at intervals, but Bianca sends him off to tune again until she has finished her conversation with Lucentio. Lucentio concludes and Hortensio returns to try his own hand at wooing Bianca. He gives her a sheet with a “gamut,” or scale, of notes on it, with romantic words cleverly inserted to indicate his true intention. Hortensio’s words take a different tone, though. While Lucentio was confident and coy, Hortensio pleads almost pitifully: “show pity, or I die” (III.i.76). Bianca resists his attempt more directly, failing to give the playful glimmer of hope she afforded Lucentio. Before Hortensio can respond, a servant enters, calling upon Bianca to prepare for her sister’s wedding the next day. Lucentio also leaves, and Hortensio, alone, considers the signals he received from Bianca. He sees clearly that Lucentio is infatuated with Bianca. But he does not yet know what her intentions are, and he suspects that his own chances might be slim. Preparing for the possibility of rejection, his former enthusiasm dwindles, and he tells himself that he will simply find another wife if Bianca proves unwilling.

Analysis: Act III, scene i

Despite the unorthodox presence of the Induction and the story of Christopher Sly, the narrative form of The Taming of the Shrew is generally extremely straightforward. It follows the two plots initiated in Act I, scene i: the main plot, involving Katherine’s wooing and marriage, and the subplot, involving Bianca’s wooing and marriage. This scene offers a diversion from the main plot by turning to the subplot—the wooing of Bianca by her competing suitors.

In Act III, scene i, the play continues to verbally excite as well as explore deeper aspects of love and marriage. Like the argument between Petruchio and Kate in the last scene, the exchange between Lucentio and Bianca displays Shakespeare’s considerable skill with puns. It also subtly explores the idea of women in marriage again, this time by contrasting how Lucentio and Hortensio treat Bianca.

type of error:

the error in the sentence is a "dangling modifier". a dangling modifier is a phrase, word or clause that "dangles" because there is not target to modify. in this case, "after mopping the floor" is the dangling modifier since it has no word to modify. the noun "house" cannot mop the floor; therefore there is a mistake in the writing of the sentence.